On the Performance Gap Between ML and Iterative Decoding of Finite-Length Turbo-Coded BICM in MIMO Systems

As real-time applications typically require short length code words, this paper analyzes the minimum achievable code word error rate of the given finite-length code words, namely, maximum likelihood (ML) decoding error probability. For coding schemes ML decoding is too complex, the key contribution of this paper is to analytically assess the performance gap between ML decoding and a practical decoding scheme. We analyze the combination of turbo codes and bit-interleaved coded-modulation that is a spectrally efficient coding scheme adopted in 3GPP long term evolution (LTE). In single-input single-output (SISO) systems, it was shown in the literature that turbo decoding delivers near-ML decoding performance. In this paper, we extend the analysis to a multi-input multi-output (MIMO) system. In contrast to the SISO case, the turbo principle-based iterative decoding scheme is subject to appreciable performance loss compared with the ML decoding, even in good MIMO channel conditions. For this reason, we further analyze potential reasons and examine possible improvements. By means of simulation, it is shown that convergence to a non-ML code word rather than non-convergence is the key reason for the observed performance loss in good channel conditions.